Before describing the prior art, it is useful to specify hereinbelow the concept of figure of merit of a mechanical resonator.
In a USO, the mechanical resonator is associated with an oscillating electronic loop which makes it possible to maintain the vibration of the resonator at its mechanical resonance frequency. Thus, the stability of the frequency of the alternating electrical signal present in the electronic loop benefits from the stability of the frequency of the mechanical resonance of the resonator, generally much greater than that of a purely electronic oscillating loop.
The stability of the resonance frequency the mechanical resonator is all the greater when the figure of merit of the resonance vibration is high, in other words the vibration energy contained in the resonator is great compared to the energy lost per period of the vibration. There are two types of energy losses, on the one hand the intrinsic losses due for example to the viscous damping of the material forming the resonator, on the other hand the extrinsic losses due for example to a gaseous damping or to an inappropriate fixing of the resonator. This is why the best resonators are produced in materials with very low viscous damping such as quartz, why they are vacuum-packaged in a package, and why they are fixed in this package in the u position of what has come to be called ideally a vibration node.
There is a practical formulation for expressing the contribution of the different sources of energy losses, as is explained hereinbelow.
The expression of the real figure of merit of the resonator is written:Q real=2π·E/ΔE Where E is the energy contained in the resonator and ΔE the energy lost per period of the vibration. For the examples cited previously, ΔE can be written:ΔE=ΔE intrinsic+ΔE gas+ΔE fixing
It is therefore possible to write:1/Q real=(ΔE intrinsic+ΔE gas+ΔE fixing)/2π·E Or:1/Q real=ΔE intrinsic/2π·E+ΔE gas/2π·E+ΔE fixing/2π·E 
Thus , it is possible to associate with each source of energy losses a figure of merit which is specific to it, and write:1/Q real=1/Q intrinsic+1/Q gas+1/Q fixing
For the real figure of merit of the resonator to be close to its intrinsic figure of merit, it is therefore essential for the figures of merit associated with the various extrinsic sources of losses to be very much greater than the intrinsic figure of merit. By way of example, if Q intrinsic is of the order of 106, it is desirable for Q fixing and Q gas to he of the order of at least 107.
The invention relates to the losses due to the fixing of the resonator, and aims to obtain Q fixing very much greater than Q intrinsic, while benefiting from a very small bulk and a very low production cost.
The closest prior art combines the following two approaches. For the first approach, as for the invention, the vibration of the resonator is an expansion-compression mode. For the second approach, the vibration of the resonator is a contour mode, which means that the structure of the vibrating part of the resonator is planar and that the vibrations take place primarily parallel to its plane; there can be, for example, expansion-compression or shearing vibrations or bending oscillations.
The first approach (patent application No. FR 2 962 614 published on 13 Jan. 2012 in the name of the applicant) is illustrated in FIG. 1A intended to explain the operation of the vibrating core 10 of the resonator, and in FIG. 1B which shows a perspective view in longitudinal cross section of the resonator comprising the vibrating core 10 and a hollow straight cylinder CC of square directrices surrounding the vibrating core 10 and intended to be assembled on a package base EB.
Referring to FIG. 1A, the vibrating core 10 of the resonator comprises a solid straight cylinder R, a hollow straight cylinder 2 of the same height surrounding the solid straight cylinder, and a membrane 1 positioned in the median plane π and secured to the cylindrical surface of the solid cylinder and to the internal cylindrical surface of the hollow cylinder.
The solid cylinder R vibrates according to a longitudinal expansion-compression resonance mode and has a vibration node N situated in the median plane π, and the hollow cylinder 2 vibrates also in longitudinal expansion-compression resonance mode, at the same frequency as the solid cylinder, but in phase opposition with the vibration of the solid cylinder. The identity of the resonance frequencies of the two cylinders stems from the identity of their heights, which is a condition necessary to the operation of the resonator (see page 9, line 37 to page 10, line 11 of the abovementioned patent). The vibrations in phase opposition of the two cylinders correspond to a particular mechanical resonance mode of the vibrating core 10, that is to say a spontaneous mode.
The weight of the hollow cylinder 2 is very much greater than the weight of the solid cylinder R, because the thickness of the wall of the hollow cylinder is of the order of magnitude of the diameter of the solid cylinder (see page 12, line 2 to line 9). This geometrical condition in fact means that the weight of the hollow cylinder 2 is of the order of 10 times the weight of the solid cylinder R.
It follows therefrom that the vibration amplitude of the hollow cylinder is very much less than that of the solid cylinder, in order for the quantities of movement involved in said particular resonance mode to balance naturally (see page 10 line 14 to line 22). This makes it possible for the effects of the radial deformations (Poisson effects) of the two cylinders to be neutralized in a zone ZF situated on the outer surface of the hollow cylinder in the vicinity of the median plane π.
Thus, the zone ZF can be practically decoupled from the vibration of the resonator, which makes it possible, as shown in FIG. 1B, to hold the hollow cylinder 2 by means of bridges P secured to a hollow cylinder CC without affecting the intrinsic figure of merit of the resonator. The operation of this resonator known from the prior art is thus very satisfactory.
The teaching of the first approach is moreover complemented in the article entitled “A Micro-Resonator for Fundamental Physics Experiments and its Possible Interest for Time and Frequency Applicaitons” by Olivier Le Traon (European Frequency and Time Forum, 2011) which indicates that the expansion-compression of the hollow cylinder is accompanied by a bending of its wail (FIG. 4 of the article and last line of section II), thus demonstrating that the real behavior of the vibrating core of the resonator is a little more complex than the basic principle presented in the abovementioned patent.
The drawbacks of this first approach lie firstly in the bulk of the resonator due to its three-dimensional structure that is ill suited to the techniques of integration of microsystems whose structures are generally planar; secondly, the correct operation of the resonator is demanding with respect to the symmetry of the resonator relative to the median plane π, particularly with respect to the position of the membrane 1 obtained by controlling the depth of the machining performed parallel to the longitudinal axis Δ of the resonator which weighs on the production cost.
It could appear interesting to take a lead from this first approach by trying to make a planar vibrating core structure operate on a mode similar to that described in the first approach, as illustrated in FIG. 1A′ which shows said planar structure referenced 10′ comprising a bar R and two beams 2′ positioned on either side of the bar.
In order to comply with the conditions recommended. by the abovementioned patent, the beams 2′ should have the same height as that of the bar and a weight very much greater than that of the bar, which would mean, for the beams 2′, a very large dimension taken in the plane of the structure at right angles to their height dimension, as is illustrated in FIG. 1A′.
Thus, this novel approach, although benefiting from the advantage of a planar structure, would present, as for the first approach, the drawback of a significant bulk.
It might also appear interesting to take a lead only from FIG. 1A of the first approach, without complying with the recommended condition of a weight ratio between the beams and the bar. This would lead to trying to make a planar vibrating core structure 10″ like that illustrated in FIG. 1A″ operate. A study performed by means of numerical simulations (finite elements) shows that, generally, this novel approach does not work. As illustrated in FIG. 1A′″, each of the beams 2″ vibrates in expansion-compression resonance in phase opposition with the expansion-compression resonance of the bar R, but the Poisson effects of the beams do not neutralize those of the bar. More specifically, the Poisson effects of the beams have amplitudes close to those of the Poisson effects of the bar, but are of a direction opposite to the Poisson effects of the bar; in other words, the Poisson effects of the beams “accompany” the Poisson effects of the bar. Because of this, the longitudinal central axis δ of each of the beams remains practically immobile during the vibration. In these conditions, the symmetry of each of the beams and of its vibration leads, in the same way as for the bar, to the existence of a vibration node n situated at the center of the beam, that is to say at the core of the material. Because of this, the vibrating core does not exhibit any zone that makes it possible to hold it without affecting the intrinsic figure of merit of the resonator.
The second approach of the closest prior art is shown in the U.S. Pat. No. 4,350,918 published on 21 Sep. 1982 in the name of Kabushiki Kaisha Daini Seikosha and illustrated in FIGS. 2A, 2B and 2C and 2D (FIGS. 8, 9, 10b and 10c of the patent).
FIG. 2A shows a front view of a piezoelectric resonator 21 with contour vibration mode comprising a vibrating portion 26 and at least one support portion 25 forming a piece with the vibrating portion by means of a bridge part 31. The resonator 21 is characterized. in that each support portion 25 consists of an elastic part 30 interconnected with said vibrating portion 26, an attenuation part 28 made of a piece with said elastic part 30 and with only minimal displacement and a fixing part 27 intended to be fixed to a support piece.
The attenuation part 28 is connected by its two ends to the elastic part 30 via connection parts 29, thus forming an opening in the support portion 25.
The width of the bridge part 31, the width of the elastic part 30, the width of the attenuation part 28, the distance between the elastic part and the attenuation part, and the length of the elastic part are respectively W0, W1, W2, W3 and L1, as shown in FIG. 2B.
These dimensions play an important role in the operation of this resonator, particularly in the decoupling of the vibrations, of the vibrating portion with respect to the fixing part 27. When these dimensions satisfy a certain number of relationships specified in the abovementioned patent, then the decoupling can be excellent as illustrated in FIGS. 2C and 2D which show only a quarter of FIG. 2A taking account of the symmetry.
FIGS. 2C and 2D show by dotted lines exaggeratedly enlarged deformations of the resonator vibrating on two contour modes respectively. It is specified that the resonator is designed to operate simultaneously on these two modes deliberately coupled together, which is obtained by observing certain dimensional ratios between the short side W and the long side L of the vibrating portion 26; this makes it possible to obtain an excellent frequency/temperature characteristic of the resonator.
To obtain the decoupling of the vibrations of the vibrating portion 26 with respect to the fixing part 27, it is therefore necessary for each of the two contour modes illustrated in FIGS. 2C and 2D to be decoupled from said fixing part. This is what is obtained by means of this second approach, because the displacement of the fixing part 27 is minimal for the two modes.
The teaching of the second approach is moreover complemented in the article entitled “Design and Fabrication of Length-Extensional Mode Rectangular X-Cut Quartz Resonator with Zero Temperature Coefficient” by Yukio Yokoyama (IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 53, No. 5, May 2006) which presents a resonator suitable for vibrating according to a longitudinal expansion-compression mode and illustrated in FIG. 2A′ (FIG. 9 of the article).
Although the article is very inexplicit on the operation of this resonator (a few lines at the end of the conclusion), a person skilled in the art can recognize the device of the second approach illustrated in FIG. 2A, and understand that the author of the article has adapted the second approach to the particular case of a resonator vibrating on a single contour mode, in this case the longitudinal expansion-compression mode.
The planar structures of the resonators of the second approach and their exclusively open-ended machinings are well suited to the microsystems integration techniques.
However, the drawback of this second approach relates to the difficulty in producing the resonator with sufficient accuracy to ensure correct operation, notably in the support portions 25 and more specifically with respect to the widths W1 and W2 of the elastic part and of the attenuation part respectively, as well as the distance W3 between the elastic part and the attenuation part. This production difficulty, all the greater when the dimensions of the resonator are small, is reflected either by a brake to the miniaturization of the resonator, or by a relatively high production cost.
The aim of the invention is notably to overcome the drawbacks of the earlier approaches by proposing a mechanical resonator whose operation is as satisfactory as that obtained by the first and second approaches, but whose structure is better suited to reducing the bulk and the cost of the resonator.
To obtain a good understanding of the elements characterizing the invention, it is useful to recall that the slenderness ratio of a parallelepipedal beam, taken in a plane borne by its length dimension L and one of its two section dimensions c, is defined by the ratio L/c.